Answer the questions below about Line 1 and Line 2 shown below. 

left parenthesis, 4, dot, 8, right parenthesis, dot, 3

(4⋅8)⋅3

Line 1

4, dot, left parenthesis, 8, dot, 3, right parenthesis

4⋅(8⋅3)

Line 2

Answer

Attempt 1 out of 2

The expression was rewritten using the  Commutative Property of AdditionAssociative Property of MultiplicationCommutative Property of MultiplicationDistributive PropertyAssociative Property of Addition.
left parenthesis, 4, dot, 8, right parenthesis, dot, 3(4⋅8)⋅3 equals  dot, 3⋅3 which equals .4, dot, left parenthesis, 8, dot, 3, right parenthesis4⋅(8⋅3) equals 4, dot4⋅  which equals .

The two lines presented show different ways of grouping the factors in the expression \( (4 \cdot 8) \cdot 3 \) and \( 4 \cdot (8 \cdot 3) \). The grouping has changed, but the result will be the same. This transformation is due to the **Associative Property of Multiplication**, which allows you to change the grouping of numbers being multiplied without changing the product.

### Explanation:
1. **Line 1**: \( (4 \cdot 8) \cdot 3 \) means you multiply 4 and 8 first, then multiply the result by 3.
2. **Line 2**: \( 4 \cdot (8 \cdot 3) \) means you multiply 8 and 3 first, then multiply the result by 4.

Since multiplication is associative, both expressions will give the same result.

### Correct answer:
The expression was rewritten using the **Associative Property of Multiplication**.

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Would you like further details on this property, or have any other questions? 

Here are five related questions you might find interesting:
1. What is the difference between associative and commutative properties?
2. How does the distributive property differ from the associative property?
3. Can you apply the associative property to addition as well as multiplication?
4. Are there operations where the associative property does not apply?
5. How do these properties help in simplifying complex algebraic expressions?

**Tip**: The associative property is very useful when rearranging expressions to make calculations easier!

Answer the questions below about Line 1 and Line 2 shown below. (4⋅8)⋅3 Line 1 4⋅(8⋅3) Line 2

Explore how the Associative Property of Multiplication applies to the expressions (4⋅8)⋅3 and 4⋅(8⋅3). This concept is essential in algebra and demonstrates how grouping factors in multiplication does not affect the product. Suitable for students in Grades 5-7.

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